Time Petri nets (TPNs) are a popular Petri net model for specification and verification of real-time systems. A fundamental and most widely applied method for analyzing Petri nets is reachability analysis. The existing technique for reachability analysis of TPNs, however, is not suitable for timing property verification because one cannot derive end-to-end delay in task execution, an important issue for time-critical systems, from the reachability tree constructed using the technique. In this paper, we present a new reachability based analysis technique for TPNs for timing property analysis and verification that effectively addresses the problem. Our technique is based on a concept called clock-stamped state class (CS-class). With the reachability tree generated based on CS-classes, we can directly compute the end-to-end time delay in task execution. Moreover, a CS-class can be uniquely mapped to a traditional state class based on which the conventional reachability tree is constructed. Therefore, our CS-class-based analysis technique is more general than the existing technique. We show how to apply this technique to timing property verification of the TPN model of a command and control (C2) system.

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Reachability analysis of real-time systems using time Petri nets

Analysis of sequential failures for assessment of reliability and safety of manufacturing systems

Stochastic Petri nets: Properties, applications and tools

In this paper we overview some recent results obtained by the authors and collaborators on the performance bounds analysis of some stochastic Petri net systems. The mathematical model can be seen either as a result of the addition of a particular random timing interpretation to an “autonomous” Petri net or as a generalization of classical queueing networks with the addendum of a general synchronization primitive. It constitutes an adequate tool for both the validation of logical properties and the evaluation of performance measures of concurrent and distributed systems.

Structural techniques and performance bounds of stochastic Petri net models

Petri nets are a powerful technique widely used in the modeling and analysis of complex manufacturing systems and processes. Due to their capability in modeling the dynamics of the systems, Petri nets have been combined with fault tree analysis techniques to determine the average rate of occurrence of system failures. Current methods in combining Petri nets with fault trees for system failure analysis compute the average rate of occurrence of system failures by tracking the markings of the Petri net models. The limitations of these methods are that tracking the markings of a Petri net represented by a reachability tree can be very complicated as the size of the system grows. Therefore, these methods offer less flexibility in analyzing sequential failures in the system. To overcome the limitations of the current methods in applying Petri nets for system failure assessment, this paper expands and extends the concept of counters used in Petri net simulation to perform the failure and reliability analysis of complex systems. The presented method allows the system failures to be modeled using general Petri nets with inhibitor arcs and loops, which employs fewer variables than existing marking-based methods and substantially accelerates the computations. It can be applied to real system failure analysis where basic events can have different failure rates. Copyright © 2003 John Wiley & Sons, Ltd.

System failure analysis through counters of petri net models

The algorithm presented is designed to compute large degradable system reliability. These systems are modeled using nonrepetitive stochastic Petri nets. The reliability parameters are computed during the generation of the reachability graph. A criterion is given that allows the computation to be stopped as soon as a given precision is obtained. >

Reliability analysis of non repairable systems using stochastic Petri nets

Classical validation approach tries to prove that failed events (events that do not verify an user property) will never occur. Probabilistic validation relies on a partial analysis on a system model and tries to prove that the failed event occurrences, have a sufficiently low probability. An incorrect behavior is a very rare event: it is the consequence of a complex unknown operation sequence. The system to be validated is modeled by a stochastic Petri net. The sequence of transition firings which may lead to critical (failed) Petri net markings are characterized at the Petri net level. An efficient travel through the reachability graph must be able to visit these sequences to reach as quickly as possible critical markings. From the incidence matrix of the net and the specification of the properties to be fulfilled, we derive a linear system called the “decision system”. The set of the decision system solutions includes all characteristic vectors of sequences leading to critical markings. In this paper, we present the probabilistic validation of a Remote Procedure Call protocol. The goal is to evaluate the probability that the protocol satisfies the required “at most once” semantic. This model is solved using two probabilistic validation algorithms using the above principles. The first one is related to acyclic Markov graphs. A traversal technique combining a breadth and a depth first search traversal techniques is used considering only the critical trajectories. The second algorithm is a worst event driven and importance sampling simulation.

C. Fraize

Papers

Stochastic Petri nets: Properties, applications and tools

Reliability analysis of non repairable systems using stochastic Petri nets

Probabilistic Validation of a Remote Procedure Call Protocol